Question

A man fired a bullet in front of a mountain and he heard its echo after 2 seconds. After travelling a distance of 85 m towards the mountain, he fired another bullet and heard its echo after 1.5 seconds. The velocity of sound and distance between the mountain and the man when the first bullet was fired are

• A. 340m/s, 340m
• B. 340m/s, 140m `
• C. 140m/s, 340m
• D. 140m/s, 140m

Answer 1

The correct option is A 340m/s, 340m

In case I distance travelled by sound waves for echo is:
$2x=$ speed of sound $\times$ time of echo
$2x=V_5\times 2$----(1)

In case II distance travelled by sound waves for echo is:
$2(x-85)=$ speed of sound $\times$ time of echo
$2x-170=\vartheta \times 1.5$----(2)

From (1) putting value of $2x$ in (2):
${\vartheta }_5\times 2-170={\vartheta }_5\times 1.5$
$0.5{\vartheta }_5=170$
${\vartheta }_5=170$
${\vartheta }_5=170\times 2=340m/s$

Substituting $\vartheta s$ in (1):
$2x=340\times 2$
$x=340m$